To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 7 are [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]. The first few multiples they share are [21, 42, 63, 84] making 21 the smallest multiple 3 and 7 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{5 x 7}{3 x 7} \) + \( \frac{9 x 3}{7 x 3} \)

\( \frac{35}{21} \) + \( \frac{27}{21} \)

Now, because the fractions share a common denominator, you can add them:

\( \frac{35 + 27}{21} \) = \( \frac{62}{21} \) = 2\(\frac{20}{21}\)

By buying two shirts, Damon will save $24 x \( \frac{50}{100} \) = \( \frac{$24 x 50}{100} \) = \( \frac{$1200}{100} \) = $12.00 on the second shirt.

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

A number in scientific notation has the format 0.000 x 10^exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:

0.0004559 in scientific notation is 4.559 x 10^-4

The amount of flour you need is (3 - \(\frac{3}{4}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{24}{8} \) - \( \frac{6}{8} \)) cups
\( \frac{18}{8} \) cups
2\(\frac{1}{4}\) cups